... the atlas is a manifold. This is a typical mathematician's use of the word "is", and should not be confused with the normal use..

Moreover, if one selects a problem, works on it in isolation for a few years and finally solves it, there is a danger, unless the problem is very fam….

A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and int….

This attitude [the abstract method in mathematics] can be encapsulated in the following slogan: a mathematical object is what it does..

At the other end of the spectrum is, for example, graph theory, where the basic object, a graph, can be immediately comprehended. One will not get an….

Here is something Category-Theorists like: it is trivial, but not trivially trivial..

Although the prime numbers are rigidly determined, they somehow feel like experimental data..

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the pr….

It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers..